The length of country and western songs is normally distributed and has a mean of 200 seconds and a standard deviation of 40 seconds. Find the probability that a random selection of 16 songs will have mean length of 186.30 seconds or less. Assume the distribution of the lengths of the songs is normal.
A) 0.91
B) 0.41
C) 0.09
D) 0.59

Question

Quizplus · Accepted Answer

The standard error of the mean is 40/sqrt(16) = 10. The z-score for 186.30 is (186.30 - 200) / 10 = -1.37. The probability of a z-score being -1.37 or less is approximately 0.0853, which is closest to 0.09.

The Length of Country and Western Songs Is Normally Distributed